HARE AND OTHERS ON THE PROPOSITION

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1 doi: / v15n1p51 HARE AND OTHERS ON THE PROPOSITION JOHN CORCORAN University of Buffalo Abstract. History witnesses alternative approaches to the proposition. The proposition has been referred to as the object of belief, disbelief, and doubt: generally as the object of propositional attitudes, that which can be said to be believed, disbelieved, understood, etc. It has also been taken to be the object of grasping, judging, assuming, affirming, denying, and inquiring: generally as the object of propositional actions, that which can be said to be grasped, judged true or false, assumed for reasoning purposes, etc. The proposition has also been taken to be the subject of truth and falsity: generally as the subject of propositional properties, that which can be said to be true, false, tautological, informative, inconsistent, etc. It has also been taken as the subject and object of logical relations, e.g. that which can be said to imply, be implied, contradict, be contradicted, etc. Prima facie, such properties and relations are non-mental and objective. It has also been taken to be the resultants or products of propositional operations, usually mental or linguistic; e.g. judging, affirming, and denying have been held to produce propositions called judgments, affirmations, and negations, respectively. Propositions have also been taken to be certain declarative sentences. Finally, propositions have been taken to be meanings of certain declarative sentences. This essay is an informal, selective, and incomplete survey of alternative approaches to the proposition with special attention to the views of the late American philosopher Peter Hare ( ) and of those who influenced him. Keywords: Propositional actions; attitudes; operations; properties; relations. That all sound philosophy should begin with an analysis of propositions is a truth too evident, perhaps, to demand a proof. BERTRAND RUSSELL, 1900, Ch. II, p. 8. Prologue The English word proposition is ambiguous in that people use it with multiple normal meanings. Several of its meanings are vague in the sense of admitting borderline cases. Moreover, there are cases in which it is difficult to determine whether a passage using it should be interpreted as definitional or as informational: that is, whether the passage is stipulating how the word is to be used or whether the passage is making an informative statement about propositions in a sense already thought to have been established. This situation can be especially troublesome since, as Frango Nabrasa pointed out (per. comm.), the fact that a person defines a word in a certain Published by NEL Epistemology and Logic Research Group, Federal University of Santa Catarina (UFSC), Brazil.

2 52 John Corcoran sense is no evidence that they always, or ever, use it in that sense. A passage allegedly containing Aristotle s definition of proposition (protasis) 1 might exemplify both of the last two points. And it is worth reminding oneself that stating a necessary and sufficient condition for being a proposition need not be a definition. Let us begin by reviewing some of the main alternative approaches to the proposition. The proposition has been referred to as the object of belief, disbelief, and doubt: generally as the object of propositional attitudes, that which can be said to be believed, disbelieved, understood, etc. It has also been taken to be the object of grasping, judging, assuming, affirming, denying, and inquiring: generally as the object of propositional actions, that which can be said to be grasped, judged true or false, assumed for reasoning purposes, etc. Each propositional attitude and each propositional action is mental and subjective: each is a certain person s attitude or action. A person begins, performs, and ends an action in a limited time interval; a person s attitude is established at a time but then persists. Attitudes are sometimes established through actions: judging a proposition establishes an attitude of believing or disbelieving, grasping a proposition establishes an attitude of understanding in one sense of grasp and one sense of understand. The proposition has also been taken to be the subject of truth and falsity: generally as the subject of propositional properties, that which can be said to be true, false, tautological, informative, inconsistent, etc. It has also been taken as the subject and object of logical relations, e.g. that which can be said to imply, be implied, contradict, be contradicted, etc. Prima facie, such properties and relations are non-mental and objective. Certain forms of the attitude, action, property, and relation approaches complement one another. Each of the above construals admits of variations: e.g., in some cases a propositional attitude is thought to presuppose prior existence of its proposition its object, while in other cases propositions are thought to be produced by attitudes or in some other way to depend for their existence on attitudes. More generally, in some cases the proposition is thought to be ontologically prior to any attitude toward it and, conversely, in some cases the propositional attitude is thought to be ontologically prior to or concurrent with the proposition that is its object. Propositions have also been taken to be certain declarative sentences. In fact, in some contemporary literature of logic, the word sentence originally a technical term of grammar occurs repeatedly in contexts that would have called for proposition in former times (Church 1956b: 6). Of course, in such contexts the word sentence is not taken to denote uninterpreted strings of sounds or characters 2 per se. Rather it is intended to denote composites containing both strings per se and their meanings or senses. 3 In the composite sense, the word sentence in certain contemporary literature is reminiscent of if not synonymous with the word proposition as it was used in a broad segment of older literature. Finally, propositions have been taken to be meanings of certain declarative sentences. In some

3 Hare and Others on the Proposition 53 cases a meaning of such a sentence was assumed to be a structured entity so that e.g. No square is a circle has a different meaning than its converse and different than its double negation. In some cases a meaning of such a sentence was assumed to be an unstructured or amorphous entity so that e.g. No square is a circle has the same meaning as its converse and its double negation. For more on such amorphous entities devoid of logical form see my 1998 Santiago paper (Corcoran 1998). Introduction The reader who is not a historian of logic might appreciate being brought up to date somewhat. Although there are scattered passages in Plato ( BCE) and Aristotle ( BCE) 4 that deserve mention in any comprehensive discussion of the proposition, our topic concerns more recent developments. The Latin word propositio from which we get proposition was used by Boethius (c CE) to translate Aristotle s Greek word protasis. 5 In some passages in Aristotle, it makes sense today to translate protasis by the relational word premise as in premise of an argument, but in other passages a non-relational word such as sentence or proposition makes sense. In the middle ages, the word propositio was used non-relationally as we do today, but it was also used relationally: in a broad sense for premise of an argument and in a narrow sense for the so-called major premise of a two-premise syllogism (Gracia 1975: 546). It would be easy to overlook the logically important distinction between the relational and non-relational senses: every argument s premises are all propositions and conversely every proposition is a premise of an argument. The word pro-tasis is etymologically a near equivalent of pre-mise, pro-position, and ante-cedent all having positional, relational connotations now totally absent in contemporary use of proposition. Taking premise for protasis, Aristotle s statement (24a16) A protasis is a sentence affirming or denying something of something... is not a definition of premise intensionally: the relational feature is absent. Likewise, taking proposition for protasis, it is not a general definition of proposition extensionally: it is too narrow (Corcoran and Boger 2010). Some more recent history will help to set the scene. Charles Sanders Peirce ( ) endorsed a view of the proposition in the context of a view of logic he attributed to Thomas Aquinas ( ): logic concerns three operations of the Understanding Simple Apprehension, Judgment, and Reasoning (CP 4.38). According to Peirce (CP 4.39), Apprehension produces concepts, expressed by names; Judgment produces judgments, which are true or false and expressed by sentences; and Reasoning produces inferences, which are expressed by argumentations.

4 54 John Corcoran His examples include man for a name expressing a concept, Man is mortal for a sentence expressing a judgment, and I think, therefore I must exist for an argumentation expressing an inference. 6 Central to the Aquinas-Peirce view is that logic is about mental operations that produce the entities of interest in logical investigations. Thomas s three-operation view of logic brings to mind the first three of the six parts of the Organon, Aristotle s collected logical work: Categories, On Interpretation, and Prior Analytics, the third of which Aristotle referred to as On Syllogism. In the present context, it is suggestive to think of Categories as concerning concepts, On Interpretation as concerning judgments, and Prior Analytics as concerning inferences. Whether Thomas arrived at his view this way, Peirce does not say. 7 Justin Legault (per. comm.) believes that Aquinas made the association of the three operations with the three Aristotelian works but only after arriving at his three-operation view of logic. However, it is unclear whether such a mentalist view can be fairly attributed to Aristotle or even whether it is consistent with Aristotle s explicit statements. Views resembling the above have reverberated throughout the history of mainstream logic until the end of the 1800s, when they mysteriously vanished almost without a trace. In his 1874 Logik, Frege s teacher Lotze mentions concept, judgment, and syllogism as forms of thought and accordingly he divides Book I into three chapters devoted respectively to them. 8 There is only a faint trace in the highlyregarded Keynes book Formal Logic (1884, Part I, Chapter I, 6) and there is no trace whatever in the 1934 Cohen Nagel Introduction or the 1936 Tarski Introduction in German. 9 Such mentalist views dominated Medieval and Renaissance textbooks (Ashworth 1974: 26 36). And, with an interesting innovation due to the Cartesian philosopher Arnauld ( ) writing in the 1662 Port Royal Logic, these mentalist views continued to be accepted without criticism (Kneale and Kneale 1962: 315 8). The innovation was to add a fourth operation variously called ordering and method. Itis tempting to speculate that this was related to the Posterior Analytics, the fourth book of the Organon, which concerns demonstration and axiomatic method. However, the four-operation view might well be the result of dividing the third ( reasoning ) into two: (1) grasping immediate implications and (2) chaining them together directly and indirectly as in Prior Analytics. 10 The hypothesis of four mental operations seems reasonable. It seems clear that deduction requires the ability (1) to deduce conclusions immediately from finitely many premises and another ability (2) to chain immediate deductions to deduce a conclusion mediately. According to Henri Poincaré ( ): Imagine a long series of syllogisms [...] between the moment in which we first meet a proposition as a conclusion and that in which we reencounter

5 Hare and Others on the Proposition 55 it as a premise [...] some time will have elapsed [and] several links of the chain will have unrolled [...]. A mathematical demonstration is not a simple juxtaposition of syllogisms, it is syllogisms placed in certain order, and the order in which these elements are placed is much more important than the elements themselves. (Newman 1956: ) Poincaré s use of order echoes the word ordering in the Port Royal Logic. The four-operation view is found on pages 1 6 in the 1724 Logick by Isaac Watts ( ), which became the standard logic text at Oxford, Cambridge, Harvard and Yale for well over 100 years (Kennedy 1995: 134). Peirce wrote favorably of it when preparing his own logic text; he found the Watts book far superior to the books then used in colleges. Only Watts view of propositions is relevant here (1724: 142). When the Mind has got Acquaintance with Things by framing Ideas of them, it proceeds to the next Operation, and that is to compare these ideas together, and to join them by Affirmation or disjoin them by Negation, according as we find them to agree or disagree. This Act of the Mind is called Judgment [...]. As an Idea is the Result of our Conception [...], soa Proposition is the Effect of Judgment. For Watts, the joining of concepts by an act of Affirmation produces as effect a proposition not a judgment as Peirce would have it. Moreover, the disjoining of concepts by an act of Negation also produces as effect a proposition: disjoining seems to be a kind of negative joining ; perhaps just as disbelief is a kind of negative belief. These metaphors are reminiscent of Aristotle s Prior Analytics 24a16 juxtaposed with 24b16. At 24a16, the protaseis ( propositions ) not people affirm or deny something (the predicate) of something else (the subject). At 24b16, the copula joins or divides the subject and predicate. It is useful to recall the two main ways of joining belongs-to-every and belongs-to-some : the universal affirmative copula and the particular affirmative copula. Likewise, there were two main ways of disjoining belongs-to-none and does-not-belong-to-every : the universal negative copula and the particular negative copula. 11 According to Paolo Crivelli (2004: 154): Aristotle thinks that in every affirmative predicative belief one item is joined with one item, and that in every negative predicative belief one item is separated from one item. A related passage from Watts is quoted by Alonzo Church ( ) on page 26 of his 1956a Introduction to Mathematical Logic in connection with an explanation of Church s usage of the word proposition. To anticipate later developments, it could be said that more recent writers seem to use the words affirm and negate (or deny ) not for private acts that produce propositions but for public acts that purport to reveal the speaker s attitudes of belief

6 56 John Corcoran or disbelief in propositions whose prior existence is taken for granted. In an ideal case, a speaker is asked a yes-no question to which an affirmation purports to reveal belief and a negation or denial purports to reveal disbelief (cf. the first page of Frege s Negation, 1997: 347). One might speculate that Watts intends Affirmation and Negation not merely to produce propositions but also to produce attitudes of belief or disbelief in those propositions. However, his statement that we [...] join them by Affirmation or disjoin them by Negation, according as we find them to agree or disagree suggests that the attitudes of belief and disbelief somehow precede the production of the propositions a rather puzzling if not paradoxical view. This issue will receive further discussion below. Despite the plausibility and fresh insight of the four-operation view, it is the three-operation view that is found, almost in Peirce s wording, in Book II, Chapter I of Richard Whately s influential 1826 Elements of Logic. Whately begins the Chapter Of the Operations of the Mind and of Terms with the following sentence: There are three operations of the mind which are immediately concerned in argument; 1 st. Simple Apprehension, 2 nd. Judgment, 3 rd. Reasoning. This book is widely credited with reviving logic in England. It was read by most logicians writing in the 1800s: Mill, Boole, De Morgan, Jevons, and Peirce to name five. Interestingly, Peirce repeatedly claimed to have read Whately s book at the age of There is evident justification in calling these views mentalist, but there is no reason in sight for calling any of them psychologistic if this epithet implies the view that laws of logic are referred to the pre-conscious, behavioral, or physiological nature of the mind. For example, one psychologistic view entertained by Peirce is that any proposition a person s mind compels assent to once assent has been given to another is thereby a consequence of the other (Corcoran 2007). Background on Hare Peter H. Hare ( ) developed informed, original views about the proposition: some published (Hare 1969 and Hare and Madden 1975); some expressed in conversations I participated in at scores of meetings of the Buffalo Logic Colloquium and at dinners following. The published views were expository and critical responses to publications by Curt J. Ducasse ( ), a well-known presence in American logic, a founder of the Association for Symbolic Logic and its President for one term. 13 Hare was already prominent in the University of Buffalo s Philosophy Department in 1969 when I was appointed. Soon after, he became Chair. As his Associate Chair , I spent many hours with him in Buffalo and on professional trips (Corcoran et. al. 2008: 50).

7 Hare and Others on the Proposition 57 Without realizing it at the time, I assimilated many of his philosophical attitudes, interests, distinctions, and notational stipulations and much of his naturalistic philosophical framework despite his unfailingly respectful leeriness of my frank and unstinting Platonism. Even though my critical Platonism was as toughminded and non-religious as Hare s philosophy, it never became a live option for him. He knew of some of the arguments for the Platonist hypostatization of propositions (Hare and Madden 1975: 90), but at least once he dismissed them unceremoniously and without demonstrating awareness of their force (loc. cit.). His Platonistic tendencies were muted and restrained, always diluted or reinterpreted naturalistically. What he later insightfully called his irenic impulse fit well with his inclination to integrate and conciliate conflicting philosophies (Hare 2008: 357 8). His respectful and non-confrontational style made it easy for me to selectively incorporate his ideas. I thank Hare for my understanding of the philosophical centrality of the proposition as the object of belief, disbelief, and doubt. My previous education and research along paths set out by Aristotle, Boole, Tarski, and Quine had not prepared me for what Hare brought me to see: that the problem of the ontic and epistemic nature of propositions must be confronted by any comprehensive philosophy. Since learning from Hare, I have come to see the history of logic in a new perspective. Among the first things I now look for in historical logicians is awareness of the proposition as the object of the propositional attitudes, 14 the most important being belief, disbelief, and doubt not doubt in the ordinary sense of incipient disbelief, but in the philosophical sense of suspended judgment or, as Hare put it, unconsummated judgment. 15 Hare wrote that a theory of propositions should respond to the many epistemological and metaphysical... questions about the nature and status of the entities which serve as the objects of believing, [sc. disbelieving], doubting, etc. (1969: 268). 16 Framework Not only is this article about Hare s views, it uses a framework of terminology and notation adapted from his. He used single quotes and double quotes to mark a distinction: single quotes for words and other strings; double quotes for meanings 17 (1969: 267). Thus he notated a variant of the sense-referent distinction he called connotation-denotation (1969: 270). 18 E.g., in some contexts the five-letter word truth connotes the meaning truth and denotes the object truth. More saliently, for Hare (loc. cit.), the three-word sentence Hare admired Whitehead connotes the proposition Hare admired Whitehead and denotes the fact that Hare admired Whitehead. 19 The true proposition corresponds to the fact. The string, connota-

8 58 John Corcoran tion, and denotation can be thought of as the vertexes of a triangle: the relations of connoting, denoting, and corresponding as the sides, in this case. Other cases of the semiotic triangle or semantic triad are considered below. To further set the scene, I quote from page 12 of Ralph Eaton s well-known 1931 textbook General Logic, owned by Hare and known to Ducasse: it was listed in the Bibliography of Symbolic Logic published by Ducasse s ASL in the first year of his presidency. The proposition must be distinguished from the sentence, the combination of words or signs through which it is expressed; from the fact, the actual complex situation whose existence renders it true or false; and from the judgment, which affirms or denies the proposition. Hare could have accepted this, but only as an approximation needing supplementation and clarification. Concerning its supplementation, the four concepts proposition, sentence, fact, and judgment are not enough for Hare: he also distinguished the proposition from the private belief that it is true and from the statement making the belief public. During the 1960s and 1970s, Hare favored a six-sided framework recognizing propositions, sentences, facts, judgments, propositional attitudes, and speech acts although he did not use the expression speech act. Years later, I adopted much of his approach without however sharing its naturalistic metaphysics and epistemology (Corcoran 2009). It might be misleadingly general to say naturalistic the word mentalist would be more specific: he preferred to think of propositions as accusatives of certain mental activities (1969: 269), the latter an expression from the 1600s (Arnauld 1662/1964: 111) that he later updated to psychological activities (1975: 88). To reconcile this view with traditional principles he accepted, he resorted to the lame and hackneyed dodge of taking each proposition to be an equivalence class of such mental accusatives (1969: 270). 20 Concerning its clarification, Hare would have objected to Eaton s improper use of the overworked verbs affirm and deny. In one proper sense, people, not judgments, affirm or deny [sc. negate] propositions and they do so by making affirmative or negative statements. In a derived sense, a statement can be said to affirm or deny [sc. negate] the proposition. But there are other contexts into which philosophers force the words: for Aristotle, an affirmative proposition affirms the predicate of the subject (On Interpretation, VI; Prior Analytics A1). Eaton s quoted usage is not even grammatically the same as Aristotle s. Eaton used a two-place or transitive verb taking a subject and a direct object; Aristotle used a three-place or hypertransitive verb taking a subject, a direct object, and an indirect object. Hare would have noticed that Eaton s misuse suggests failure to distinguish the judgment from the assertion or statement. The judgment is always private and silent,

9 Hare and Others on the Proposition 59 and never done in writing; the assertion is normally public and done in writing or speaking. Hare and I discussed that contrast. Frege never explicitly treats it in work he published. In fact in 1879 he refers to the sign of assertion as the judgment stroke (Frege 1997: 52, 198). Throughout his published work, the necessarily private mental act of judging is often conflated with the possibly public act of asserting. Nevertheless, in his posthumous writings we find the following forthright statement italicized, but unaccompanied by any retraction (Frege 1997: 239). When we inwardly recognize that a thought is true, we are making a judgment; when we communicate this recognition, we are making an assertion. 21 However, Hare never notes that propositional attitudes such as doubting and believing are grounded in propositional actions such as grasping and judging, which seem to presuppose prior existence of propositions. He seemed to sense the chickenegg problem (1969: 269): do propositions exist through belief or does belief presuppose prior existence of propositions? Hare s peculiar use of mental activity instead of say, mental attitude for believing and disbelieving, which has the proposition as its accusative, suggests inattention to the attitude/action distinction. Attitudes and actions are mental and subjective: each is a certain person s attitude or action. However, an attitude persists after being established. In contrast, an action is completed or aborted in a limited time interval. My judging that Peter Hare had died began and ended in a limited time interval on one sad day in January 2008; but the belief, the attitude established at that time, persists and is recalled almost every day. Attitudes are sometimes established through actions: judging a proposition establishes an attitude of belief or disbelief. But attitudes do not seem to require action in order to maintain their existence. Hare s writings about propositions are sensitive to several contexts: to ordinary man-in-the-street usage, to then-current views in the logic community, and to history of logic. But he rarely gives specific bibliographic references for his normally accurate observations. E.g., he wrote the following (1969: 268). Indeed, the venerable doctrine that a proposition is the verbal expression of a judgment, unpopular as this view is among modern logicians, probably is more in accord with both man-in-the-street usage and the history of logic than Ducasse s account. This doctrine is found almost in this wording on page 75 in Richard Whately s influential 1826 Elements of Logic. The view goes back at least to the famous Port Royal Logic (1662/1964: 99, 111, 114). There can be no discussion without a shared vocabulary. If one person says Every proposition is either true or false as Hare and I do and certain others say Not every proposition is either true or false (Mill 1843/1879, V. I, Bk. II, Ch. VII, 5),

10 60 John Corcoran there need not be disagreement. The second sentence can but need not be used to deny what the first was used to affirm. 22 In order for a second speaker to contradict a first by uttering the negation of a given sentence uttered by the first, it is sufficient for the second to have used the negation to deny the very same proposition the first used the given sentence to affirm. If certain others use the word proposition for something that might change or even lose its truth-value or that has no truth-value until conclusively tested, there is no contradiction. Likewise, there is no contradiction if certain others use true in a coherence sense, in a pragmatist sense, or in an epistemic sense. Of course, one person might share another s vocabulary for purposes of discussion without adopting it. Hare s writings on propositions used a vocabulary he shared with his intended audience, which included C. J. Ducasse, E. H. Madden ( ), and R. E. Santoni to mention three. Moreover, being a historian, he was aware of writing for a specific, limited audience that shared certain presuppositions and for which certain theses were uncontested. The richer the class of shared presuppositions and uncontested theses the more fruitful a dialogue can be. These uncontested theses can serve to characterize meanings of words such as proposition occurring in them in much the same way that the axioms of geometry have sometimes been regarded as characterizing meanings of geometrical words. 23 Perhaps more aptly, holding that the word true is indefinable, Frege thought its meaning was explained by the laws of logic (1918: 290). 24 Uncontested Theses Among Hare s uncontested theses was the traditional law of excluded middle every proposition is either true or false and also the law of non-contradiction no proposition is both true and false. He was generally careful to point out a venerable doctrine he took to be contested (1969: 268). He also subscribed to the propositional attitude thesis: every object of belief, disbelief, or doubt is a proposition (1969: 268; 1975: 80). Instead of the ambiguous word object which he used roughly in the sense of patient he preferred accusative, which, though less familiar, lacks ambiguities of object. His ontological use of this normally grammatical expression is carefully chosen. He seemed to characterize or locate propositions as accusatives of the three traditional propositional attitudes. The propositional attitude thesis, so prominent in Hare and in Ducasse, is not even mentioned by Eaton 1931, whose index omits the crucial words attitude, belief, disbelief, and doubt. It would be interesting to know who first proposed it, what its historical origin is. Mill (1843/1879, V. I, Bk. I, Ch. I, 2) wrote:

11 Hare and Others on the Proposition 61 Whatever can be the object of belief, or even disbelief, must, when put into words, assume the form of a proposition. Mill s qualification would be absurd, then, unless the object of belief or disbelief not expressed in words is not a proposition: our unspoken beliefs and disbeliefs are not propositions nor are they of propositions in Mill s sense of proposition. For the record, Frege (1997: 52 4) was moving in the right direction when he discussed the content of the judgment in 1879, separating the judgment per se from its object. Even though Frege continued to give insufficient attention to the traditional propositional attitudes, by about 1918 he had distinguished the act of grasping a proposition from the act of judging it, and he distinguished the two both from the proposition which is not an act but the object thereof and from the act of asserting the proposition (1997: 329). Believing a proposition is holding it to be true; disbelieving is holding it to be false. However, as mentioned, there are two senses of the transitive verb to doubt relevant here. Doubting a proposition, in the first sense intended, is not simply neither believing nor disbelieving: it is impossible to doubt a proposition that one does not understand. Doubting is an attitude that requires an object, an accusative, toward which it is directed. Once a proposition has been grasped, the propositional attitude of understanding it has been established, and only then can we begin the process of judging. 25 When the process is completed, or consummated, to use Hare s term, the judger has a belief or disbelief. Judging the proposition to be true produces belief of it; judging the proposition to be false produces disbelief of it. But, if the process has not started or has not come to a conclusion, the judging person has doubt in this mainly philosophical sense. The converse of the propositional attitude thesis is that every proposition is the object of a definite opinion held at a certain time by a certain person. 26 Hare certainly accepted this, but he seemed reluctant to assert it (1969: 271). I put the word opinion in double quotes when I use it in the broad sense: roughly, for a proposition toward which one has one of the three classical propositional attitudes, following Ducasse and Hare (1975: 88). In this technical sense, every proposition known to be true or known to be false is an opinion of the knower. Moreover, among a person s opinions are the propositions the person grasped but did not judge. In this sense, an opinion is a belief, disbelief, or doubt, and conversely. 27 The question is not limited to traditional propositional attitudes. It concerns understanding: are there propositions that have never been understood by anyone? The venerable doctrine construed literally would yield a resounding Of course not, judgments are human creations! Arnauld (1662/1964: 111) wrote,... all mental activity can be reduced to conceiving, judging, reasoning, and ordering....

12 62 John Corcoran Hare also accepted the truth-value coherence thesis: propositions are the things that can literally and coherently be said to be true or be said to be false. He cheered Ducasse s insistence that an opinion someone s belief, disbelief, or doubt should never be said to be true or false. A person s belief or disbelief is correct if the proposition believed is true or the proposition disbelieved is false but erroneous if the proposition believed is false or the proposition disbelieved is true. And I applaud Hare, who would have been amused to know that a similar terminological nicety had been anticipated over three centuries earlier in the 1662 Port Royal Logic, which in the 1964 Dickoff James translation called a judgment correct or incorrect according as the proposition involved was true or false evidently ignoring negative judgments (Arnauld 1662/1964: 111). Although Mill praised the Port Royal Logic, he did not always learn its lessons: his stated view was that errors are false propositions (1843/1879, V. I, Bk. I, Ch. I, 2). In a later paper I hope to discuss whether Aristotle deals with the twin distinctions of true propositions from correct beliefs and of false propositions from erroneous beliefs. Respecting the truth-value coherence thesis, Ducasse does not apply true or false to sentences or to facts. Hare suggests that Ducasse s theory could accept interrelating or tying together the sentence, the proposition, and the fact in a form of the semiotic triangle. 28 The sentence is at the vertex; the connotation and the denotation are at opposite ends of the base. The sentence, composed of words, connotes the proposition, composed of meanings. If the proposition connoted is true, the sentence or propositional expression denotes the fact composed of the things the proposition is about. Hare wrote that the expression can connote a proposition while having zero denotation (i.e., the proposition expressed [sc. connoted] is false) (1969: ). 29,30 SENTENCE CONNOTATION true proposition false proposition DENOTATION state-of-affairs, fact zero, null, nothing Hare and Madden criticized Ducasse for identifying the true proposition with the fact it corresponds to (Hare and Madden 1975: 89). However, Hare and Madden never show the slightest understanding of why an intelligent person would be inclined to make this mistake nor do they ever admit that other important figures such as Frege (1918/1956) might have made it. 31 In 1918 Frege wrote (1997: 342): What is a fact? A fact is a thought [sc. proposition] that is true. In a spirit similarly lacking sympathy and respect, Austin (1961: 91) disapproves of taking fact as synonymous with true statement.

13 Hare and Others on the Proposition 63 Hare and Madden never mention the apparent interchangeability of expressions such as it is true that and it is a fact that, or is true and is a fact. In particular, they never mention contexts like the following that make it appear that certain expressions, e.g., that zero is even, apparently denoting facts also appear to denote true propositions and conversely. Zero is even. It is a fact that zero is even. It is true that zero is even. The proposition that zero is even is true. It is a true fact that zero is even. The fact is that zero is even is a known truth. The proposition that zero is even is true if and only if it is a fact that zero is even. It is remarkable, then, that they did not think to mention the many cases where fact is not replaceable by true proposition. The untimely death of Peter Hare is a sad fact. No fact can be deleted from the past. Facts can be hidden but they cannot be destroyed. Histories do not present all the facts and not all things they do present are facts. Neither Frege nor Ducasse felt any need to explain such contexts. 32 Do Frege and Ducasse agree? Ducasse might have been hypostasizing propositions while Frege might have been doing the reverse to facts. Either way, Hare and Madden s criticisms seem decisive. The thought that the universe is exhaustively composed of timeless abstractions such as true propositions seems wildly implausible. But neither Frege nor Ducasse, as far as can be determined from the Hare and Madden discussion, seemed to accept this interpretation. Moreover, as far as I can tell, there is no discussion by Frege 33 or by Ducasse of the ambiguity of the word fact. Ducasse implied that Mont Blanc is a constituent of Mont Blanc is cold (Hare 1969: 271), whereas in his posthumous writings Frege implied the contrary (1997: 293). It might seem to follow that for Frege Mont Blanc is not a constituent of the fact that Mont Blanc is cold: he might take the individual concept Mont Blanc to be a constituent of the proposition he takes to be a fact. In 1892 Frege wrote (1997: 158): A truth-value cannot be part of a thought [sc. proposition] any more than, say, the Sun can, for it is an object not a sense. Frege does not reveal awareness of ambiguities of the word fact. A more plausible interpretation of Frege is that he was simply using the word fact as synonymous with true proposition, not that he was taking facts in the sense of Eaton (supra), the things true propositions were true in virtue of to be the very

14 64 John Corcoran things that were true. My guess is that Frege never took truth-makers, Eaton s and Hare s facts, to be truth-bearers, things that are true in the most basic sense. 34 Although Frege probably meant his sentence A fact is a true proposition informatively, he would have forestalled uncertainty if he had indicated that it could have been meant definitionally (see above). It is a sad irony that Hare s beloved Peirce uses the word fact as a synonym for proposition not just true proposition in his famous 1877 article The Fixation of Belief (Peirce 1992: , esp. 113). Hare must have read that article dozens of times. But Peirce is not the only accomplished logician to do this. Tarski also uses fact where proposition would be called for. But it would be misleading to say that he uses it as a synonym for proposition, a word he studiously avoids: he even calls propositional logic sentential calculus. For occurrences of fact used where proposition would be called for, see Tarski (1941/1946: 122 and 1956/1983: 146, 158 9, 249, 385, 449). For example, in both works expressions are said to express facts, where is clear that the facts are not all true, so to speak (1941/1946: 122 and 1956/1983: 385). Ambiguity of not To deny a statement is to affirm another statement, known as the negation or contradictory of the first. W.V. Quine, Methods of Logic, 1959: 1. Hare, attuned to the importance of ambiguity in philosophical dialogue, recognized two senses of the word not. In one sense not is used for the familiar internal truthfunctional negation as in teaching is not just a job. Sometimes not in this sense is synonymously interchangeable with it is not the case that as in if not every teacher is happy, some teacher is unhappy. When used in this sense to make a statement, it expresses part of the proposition stated, a part that is internal to the proposition while in no way indicating the speaker s propositional attitude, which is external. In another sense it indicates that the speaker intends to deny something (1969: 267) and thus has the attitude of disbelief toward that something. The sentence not every number is even might be used to affirm a negation to affirm the negative proposition it is not the case... or to deny a universal to deny the general proposition every number... ). In the first sense, which I call the truth-functional sense, the constitutive sense, or the internal sense, it indicates a feature of the logical form of the proposition expressed; it indicates a constituent internal to the proposition. 35 It is internal to the proposition. In some simple cases, inserting or deleting an occurrence of such a not reverses truth-value. Thinking that this is always the case leads to the fallacy of single nega-

15 Hare and Others on the Proposition 65 tion: some number is even and some number is not even are both true. In the second sense, which I call the attitudinal sense, the rejective sense, or the external sense, it indicates a feature of the speaker s attitude but has no bearing on logical form of the proposition expressed: it is external to the proposition. The word not is never used in the external sense when it occurs in a clause of a larger sentence as in the following. 36 If not every number is even, then some number is not even. Zero is not odd and one is not even. Every number that is not even is odd. In all such occurrences, it contributes to expression of a part of the proposition that the sentence is used to affirm. This is so even if it is repeated as in if two is even, it is not the case that it is not the case that two is even. Of course, the proposition expressed has the same truth-value as the one expressed by deleting the repeated it is not the case that. An occurrence of not being used by a speaker to indicate denial of a proposition is used in what I called the attitudinal sense. However, in this case its meaning is not part of the proposition denied any more than the meaning of is it the case that is part of the proposition questioned using a sentence beginning therewith or that the meaning of the question mark is part of the proposition questioned. Hare thought that Ducasse meant to say that the attitudinal sense never occurs as part of a proposition (1969: 267). 37 Hare is the first person I know of to recognize the distinction between the truthfunctional and attitudinal senses of negative expressions such as not and it is not the case that. Along with this goes recognition that denying a proposition is not the same act as affirming the negation of a proposition. The truth-functional negation is not used to deny a proposition. As Aristotle first noted in Chapter VI of On Interpretation, whatever is the object of an act of affirming can be the object of an act of denying and whatever is the object of an act of denying can be the object of an act of affirming: affirming and denying apply to the same things propositions. In order to clarify the fact that I am not giving Hare too much credit, I should note that in 1879 Frege has a very closely related distinction: roughly, between negatively judging a proposition devoid of negations and affirmatively judging the negation of such a proposition (1997: 54 5). However, later he abrogates virtually all ground for credit by repeatedly and improperly using is denied where no denying or judging is relevant (1997: 56, 60), as I note below. The declarative 38 [sentence] type covers two subtypes: the assentive and the dissentive. A declarative sentence is one characteristically used to make a statement, an imperative sentence is one characteristically used to make a command,

16 66 John Corcoran and an interrogative sentence is one characteristically used to make an inquiry (Lyons 1977, vol.1: 30). It is useful to consider the interrogative type along with the declarative. Compare Lyons 1977, vol. 2: Interrogative: Assentive: Dissentive: Is it the case that 1000! + 1 is prime? It is the case that 1000! + 1 is prime. It is not the case that 1000! + 1 is prime. The three speech acts that use these three sentences are performed on one and the same proposition. 39 The interrogative sentence can be used to express curiosity or philosophical doubt in or toward the same proposition that the assentive is used to express belief in and the dissentive is used to express disbelief in. Being an inquiry is clearly a property of a speech-act and not of the proposition that is the object of the act. Likewise, being an acceptance is primarily a property of a speech-act and not of the proposition that is the object of the act. A person may accept any proposition whether affirmative such as Every prime exceeds one or negative such as No prime precedes two. As Hare points out, being a rejection is primarily a property of a speech-act and not of the proposition that is rejected. A person may reject any proposition whether affirmative or negative, echoing Aristotle s point alluded to above. There are cases of course where the interrogative preamble is it the case that is omitted and the inquiry is indicated simply by the question mark or, in speech, by intonation. At least as common are cases where the affirmative preamble it is the case that is omitted and the acceptance is signaled in speech by intonation or in writing by punctuation. There are even cases of course where the negative preamble it is not the case that is omitted and the rejection is indicated simply by the context or, in speech, by ironic intonation. Recently I overheard a colleague say That s a wonderful idea in such a tone that it was clear the opposite was meant. Are there cases where an acceptance is made using an interrogative type sentence? Of course. Some of these use what are known as rhetorical questions. 40 It goes without saying that the assentive preamble is subject to an ambiguity similar to that of the dissentive: instead of signaling assent it can be intended as empty rhetoric. This is especially common when it occurs inside the sentence as in if 1000! + 1 is not prime, then it is the case that a smaller number is a prime factor of 1000! + 1. An important difference between the truth-functional and the attitudinal interpretations of the ambiguous negative preamble it is not the case that concerns their roles in dialogue. If the first speaker makes a statement without preamble, the second can express disbelief using a dissentive, the same sentence with the negative preamble.

17 Hare and Others on the Proposition 67 A: 1000! + 1 is prime. B: It is not the case that 1000! + 1 is prime. However, if the first speaker s statement was dissentive, it would not be open to the second speaker to simply affix the negative preamble to the second as follows. A: It is not the case that 1000! + 1 is prime. B: It is not the case that it is not the case that 1000! + 1 is prime. The second speaker is not contradicting the first: the second is not implying that 1000! +1 is prime. The second s point has to do with the second s state of mind, not with the nature of 1000! + 1. It is clear that A s statement in the second example implicates that A disbelieves that 1000! + 1 is prime. The question arises whether the same statement can be made using I disbelieve that 1000! + 1 is prime. More generally, the question is whether the preamble I disbelieve that is exactly synonymous with the preamble It is not the case that in the attitudinal sense. Another important difference between the truth-functional and the attitudinal interpretations of the ambiguous negative preamble it is not the case that concerns the double negation, e.g., the following: It is not the case that it is not the case that 1000! + 1 is prime. In the truth-functional sense, this could be used to assert a proposition having the same truth-value as the proposition that 1000! +1 is prime, as said above. But in the attitudinal sense, things are different. In the first place, it is not the case that denying that I am denying that 1000! +1 is prime is asserting that 1000! +1 is prime. Rather, denying that I am denying that 1000! +1 is prime is much weaker; it reveals very little about my attitude toward the proposition that 1000! +1 is prime. In fact, if someone were to ask me whether I deny that 1000! +1 is prime, I might well reply as follows. I deny that I deny that that 1000! +1 is prime. However, it is not clear to me whether the last sentence could be used as a conversational equivalent to the above double negation taken attitudinally. Anyway, asserting the double negation of a proposition is not achieved by double denying it or denying its denial. In the usual symbolic languages, there are no attitudinal preambles such as is it the case that, it is the case that, it is not the case that. In such languages, absolutely every sentence is a component of larger sentences and therefore every

18 68 John Corcoran occurrence of a negation sign is truth-functional: no occurrence of a negation sign is attitudinal. However, in 1879 Frege did not always seem recognize the difference. He apparently thought that propositions involving truth-functional negation really involve nested denials. He writes as if his asserting not every number is even was his asserting that he was denying that for every number he was denying that it was even. He seemed deliberately and repeatedly to write is denied where it is not the case would have been more to the point and to write is affirmed where it is the case (or nothing) would have been more to the point (1997: 52 75). In the 1918 Frege papers, which Hare probably did not read, there are many points that touch on themes Hare wrote about. E.g., Frege (1918/1956: 293) noticed that the same proposition is asserted whether an assentive sentence is used with or without an assentive preamble: it is the case that 1000! + 1 is prime is the same proposition as 1000!+1 is prime. Unfortunately, the only assentive preamble Frege considered was the ambiguous it is true that, which can also be used not as a preamble but to ascribe truth to the proposition. And worse, he failed to notice the ambiguity and, perhaps as a result, he mistakenly thought that ascribing truth did not change the proposition either. After all, whereas it is the case that 1000! + 1 is prime can be used to assert a proposition about a certain number and not about a proposition, the sentence the proposition that 1000! + 1 is prime is true can also be used to make an assertion about a proposition and not about a number. The proposition about the number 1000! + 1 is expressed in the object language. The proposition about the proposition is expressed in the metalanguage. Moreover, as I only recently noticed, Frege (1997: 355) comes close to Hare s distinction between the truth-functional and the attitudinal not even though he never explicitly discussed propositional attitudes and he rarely used the words belief and disbelief in the relevant senses. Hare (1969: 267) considers a statement made using the ambiguous sentence God does not exist. On Hare s view this might be construed in at least three ways: as (1) a rejection, denying the affirmative proposition that God exists or as acceptance of either of two propositions: (2) acceptance that it is not the case that God exists affirming the negation of an affirmative or (3) acceptance that God is nonexistent affirming an affirmative having a negative predicate adjective. The difference between 2 and 3 is analogous to one of the differences described using the expressions de dicto and de re. On one analysis, statement uses the attitudinal negation (1); use the truth-functional (2) and (3). Hare has taken a step past the position suggested by Santoni (1969: 258). 41